In what follows, we review the main elements of the perturbative
QG, referring to the recent textbook [1]} for most of the
technical details. First of all, we consider the choice of the
action and the corresponding gauge-fixing conditions, mostly,
in the framework of the background field method
[2]}, [3]} (the reader can find more references
starting from these two). After that, we review the structure of
propagator of the metric perturbations in various models and the
corresponding analysis of the degrees of freedom in QG.
